Finite Group Databasebeta

← #18006382

Subgroups — #18006382

Order 4736.

454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558341C212yesmaximal, complemented
2#14558335C211yesmaximal, characteristic, complemented
3#14557918C211yesmaximal, characteristic, complemented
4#14557805C211yesmaximal, characteristic, complemented
5#14557803C211yesmaximal, characteristic, complemented
6#14557798C212yesmaximal, complemented
7#14557709C212yesmaximal, complemented
8#14557706C212yesmaximal, complemented
9#14557650C211yesmaximal, characteristic, complemented
10#14557648C211yesmaximal, characteristic, complemented
11C37×#578C211yesmaximal, characteristic, complemented
12#11924582C2212yes—
13#11924567—22no—
14#11924567C2212yes—
15#11924563—22no—
16#11924561—22no—
17#11924561C2212yes—
18#11924561C2212yescomplemented
19#11924559—21no—
20#11924556—22no—
21#11924556C2211yescharacteristic
22C2×#10596941—22no—
23C2×#10596941C2212yescomplemented
24C2×D296C2211yescharacteristic
25D8×D37—21no—
26#11924543C2212yescomplemented
27#11924542C2211yescharacteristic
28#11924525C2212yescomplemented
29#11924472C2211yescharacteristic, complemented
30#11924471C2211yescharacteristic, complemented
31#11924463C2211yescharacteristic, complemented
32#11924463C2212yescomplemented
33#11924462C2211yescharacteristic
34#11924455C2212yescomplemented
35#11924452C2212yescomplemented
36C8×Dic37C2211yescharacteristic, complemented
372−1+4×C37C2212yescomplemented
38#137×C37—22no—
39#137×C37C2212yescomplemented
40#135×C37—21no—
41#135×C37C2211yescharacteristic
42C2×Q16×C37—21no—
43C2×Q16×C37C2211yescharacteristic, complemented
44#131×C37C2211yescharacteristic, complemented
45#41×C37—22no—
46#41×C37—22no—
47#41×C37—42no—
48#41×C37C2312yes—
49#41×C37C2311yescharacteristic
50C2×Q8×C37—22no—
51C2×Q8×C37—22no—
52C2×Q8×C37C2312yes—
53#10596966—22no—
54D4×D37—22no—
55D4×D37—42no—
56#10596962—22no—
57#10596962C2311yescharacteristic
58C2×D148—22no—
59C2×D148C2312yes—
60Q16×C37—22no—
61Q16×C37—21no—
62Q16×C37—21no—
63Q16×C37D411yescharacteristic
64SD16×C37—22no—
65SD16×C37D412yes—
66D8×C37D411yescharacteristic
67M16×C37—21no—
68M16×C37C2311yescharacteristic
69C2×C8×C37—21no—
70C2×C8×C37C2311yescharacteristic
71#10596942—22no—
72#10596942D411yescharacteristic
73#10596941—22no—
74#10596941—22no—
75#10596941—22no—
76#10596941—22no—
77#10596941—22no—
78#10596941D411yescharacteristic
79#10596940D411yescharacteristic
80#10596939—22no—
81#10596939—22no—
82#10596939D411yescharacteristic
83#10596938—42no—
84C4×Dic37C2311yescharacteristic
85#10596934—22no—
86#10596934C2311yescharacteristic
87#10596934C2312yes—
88C2×#64436—22no—
89C2×#64436C2311yescharacteristic
90D296—21no—
91D296—21no—
92#10596929—21no—
93C8×D37—21no—
94C22×D37—22no—
95C22×D37—42no—
96Q8×C37—22no—
97Q8×C37—22no—
98Q8×C37—42no—
99Q8×C37C2×D411yescharacteristic
100Q8×C37C2×D412yes—
101D4×C37—22no—
102D4×C37—21no—
103D4×C37—42no—
104D4×C37C2×D411yescharacteristic
105D4×C37C2×D412yes—
106C2×C4×C37—22no—
107C2×C4×C37—21no—
108C2×C4×C37—22no—
109C2×C4×C37—42no—
110C2×C4×C37—42no—
111C2×C4×C37C2411yescharacteristic
112C22⋊D37—21no—
113C22⋊D37—42no—
114C2×Dic37—21no—
115D148—22no—
116D148—22no—
117D148—42no—
118D148C2×D411yescharacteristic
119C4×D37—21no—
120C4×D37—42no—
121Dic74C2×D411yescharacteristic
122C8×C37—21no—
123C8×C37C2×D411yescharacteristic
124C8×C37C2×D411yescharacteristic
125#64436—21no—
126#64436—22no—
127#64436C2×D411yescharacteristic
128#64436C2×D411yescharacteristic
129C22×C37—22no—
130C22×C37—21no—
131C22×C37H(5,𝔽2)11yescharacteristic
132C2×D37—21no—
133C2×D37—42no—
134C2×D37—82no—
135C2×D37—162no—
136C4×C37—22no—
137C4×C37—21no—
138C4×C37—42no—
139C4×C37C22×D411yescharacteristic
140C4×C37C22×D411yescharacteristic
141Dic37—21no—
142Dic37—41no—
143#3290—371nomaximal, Sylow
144C2×C37—21no—
145C2×C37—42no—
146C2×C37—41no—
147C2×C37D4211yescharacteristic
148D37—41no—
149D37—82no—
150#578D3711yescharacteristic, complemented
151#577—372no—
152#576—371no—
153#495—371no—
154#473—371no—
155#472—371no—
156#471—372no—
157#455—372no—
158#454—372no—
159#443—371no—
160#443—371no—
161C37#329011yescharacteristic, complemented, Sylow
1622−1+4C2×D3712yescomplemented
163H(5,𝔽2)—372no—
164#137—22no—
165#137—372no—
166#137—742no—
167#137C2×D3712yescomplemented
168AGL(1,ℤ/8)—372no—
169AGL(1,ℤ/8)—372no—
170AGL(1,ℤ/8)—742no—
171AGL(1,ℤ/8)—742no—
172#135—21no—
173#135—371no—
174#135—742no—
175#135—741no—
176#135C2×D3711yescharacteristic
177C2×Q16—21no—
178C2×Q16C2×D3711yescharacteristic, complemented
179C2×SD16—372no—
180C2×SD16—742no—
181C2×D8—371no—
182C2×D8—741no—
183#131—372no—
184#131—371no—
185#131C2×D3711yescharacteristic, complemented
186#124—372no—
187#108—371no—
188#108—371no—
189#104—371no—
190#104—372no—
191#104—371no—
192#101—372no—
193#100—372no—
194C4×C8—371no—
195#41—22no—
196#41—22no—
197#41—42no—
198#41—371no—
199#41—742no—
200#41—742no—
201#41C22×D3711yescharacteristic
202#41C22×D3712yes—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8C22×D3712yes—
206C2×D4—372no—
207C2×D4—742no—
208C2×D4—742no—
209C2×D4—1482no—
210Q16—22no—
211Q16—21no—
212Q16—21no—
213Q16—371no—
214Q16—742no—
215Q16C22⋊D3711yescharacteristic
216SD16—22no—
217SD16—371no—
218SD16—371no—
219SD16—742no—
220SD16—742no—
221SD16—742no—
222SD16—742no—
223SD16—742no—
224SD16C22⋊D3712yes—
225D8—371no—
226D8—742no—
227D8—742no—
228D8—741no—
229D8—741no—
230D8C22⋊D3711yescharacteristic
231M16—21no—
232M16—372no—
233M16—371no—
234M16—742no—
235M16—741no—
236M16C22×D3711yescharacteristic
237C2×C8—21no—
238C2×C8—371no—
239C2×C8—742no—
240C2×C8—741no—
241C2×C8C22×D3711yescharacteristic
242C22⋊C4—1482no—
243C42—371no—
244C23—742no—
245C23—1482no—
246Q8—22no—
247Q8—22no—
248Q8—42no—
249Q8—371no—
250Q8D4×D3711yescharacteristic
251Q8C2×C22⋊D3712yes—
252D4—22no—
253D4—21no—
254D4—42no—
255D4—371no—
256D4—741no—
257D4—742no—
258D4—742no—
259D4—1482no—
260D4—1482no—
261D4D4×D3711yescharacteristic
262D4C2×C22⋊D3712yes—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—741no—
269C2×C4—741no—
270C2×C4—1482no—
271C2×C4C23×D3711yescharacteristic
272C8—21no—
273C8—371no—
274C8—371no—
275C8—742no—
276C8—741no—
277C8C2×C22⋊D3711yescharacteristic
278C8C2×C22⋊D3711yescharacteristic
279C22—21no—
280C22—22no—
281C22—2962no—
282C22—741no—
283C22—5922no—
284C22—1482no—
285C22#1192458111yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—741no—
290C4—1481no—
291C4C2×D4×D3711yescharacteristic
292C4C22×C22⋊D3711yescharacteristic
293C2—21no—
294C2—42no—
295C2—41no—
296C2—2962no—
297C2—1481no—
298C2D4×C22⋊D3711yescharacteristic
subgroupG/H
centerC2D4×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#578C2
socleC2×C37D42
hypercenter#578D37
hypocenterC37#3290
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ #578

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14558341C2semidirect
2. #14558335C2semidirect
3. #14557918C2semidirect
4. #14557805C2semidirect
5. #14557803C2semidirect
6. #14557798C2semidirect
7. #14557709C2semidirect
8. #14557706C2semidirect
9. #14557650C2semidirect
10. #14557648C2semidirect
11. C37×#578C2semidirect
18. #11924561C22semidirect
23. C2×#10596941C22semidirect
26. #11924543C22semidirect
28. #11924525C22semidirect
29. #11924472C22semidirect
30. #11924471C22semidirect
31. #11924463C22semidirect
32. #11924463C22semidirect
34. #11924455C22semidirect
35. #11924452C22semidirect
36. C8×Dic37C22semidirect
37. 2−1+4×C37C22semidirect
39. #137×C37C22semidirect
43. C2×Q16×C37C22semidirect
44. #131×C37C22semidirect
150. #578D37semidirect
161. C37#3290semidirect
162. 2−1+4C2×D37semidirect
167. #137C2×D37semidirect
178. C2×Q16C2×D37semidirect
185. #131C2×D37semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145583412
#145583352
#145579182
#145578052
#145578032
#145577982
#145577092
#145577062
#145576502
#145576482
C37×#5782
#329037